Acid fracturing stimulation is one of the preferred methods to improve well productivity in carbonate reservoirs. Acid is injected into the fractured zone after a starter fracture is created in the near wellbore area by viscous fluid (pad). This results in propagation of a two-wing crack away from the perforations with simultaneous dissolution etching of the created surfaces. If the created etched surface is non-uniform, then after the treatment ends and the fracture face closes, a high conductivity path may remain in the formation, connected to the well. The important factors controlling the effectiveness of acid fracturing are the etched-fracture penetration and conductivity. In this research, I use the distributed volumetric sources (DVS) method to calculate gas production from a well stimulated by acid fracturing. The novel concept realized in this research is that, during the production process, the conductivity of the acid created fracture changes. I use the Nierode - Kruk correlation to describe this effect as a function of effective closure stress that in turn is determined from the flowing bottomhole pressure and minimum horizontal stress. By combining the well productivity calculation from the DVS method taking into account varying fracture conductivity with gas material balance, I obtain an improved model of gas production. The model is then used to not only forecast production from acid fractured wells but also to evaluate the known production history of such wells. Based on the concepts discussed above, I have developed a program called "Gas Acid" which is useful to optimize acid fracturing treatments and also suitable to infer created fracture parameters from known production history. The "Gas Acid" program has been validated with data from two Saudi Aramco gas wells. It was found that the production forecast obtained from the "Gas Acid" program matches the actual production history with reasonable accuracy and the remaining discrepancy could be resolved by taking into account refinement of the material balance. The refinement became necessary, because the "Gas Acid" program was developed for dry gas but the reservoir fluids in the field examples were classified as retrograde gas and wet gas. When accounting for the additional mass of gas "hidden" in the produced condensate, the match of forecast and actual data was improved considerably.

This work introduces the method of Distributed Volumetric Sources (DVS) to solve the transient and pseudosteady-state flow of fluids in a rectilinear reservoir with closed boundaries. The development and validation of the DVS solution for simple well/fracture configurations and its extension to predict the pressure and productivity behavior of complex well/fracture systems are the primary objectives of this research. In its simplest form, the DVS method is based on the calculation of the response for a closed rectilinear system to an instantaneous change in a rectilinear, uniform volumetric source inside the reservoir. Integration of this response over the time provides us with the solution to a continuous change (constantrate pressure response). Using the traditional material balance equations and the DVS pressure response of the system, we can calculate the productivity index of the system in both transient and pseudosteadystate flow periods, which enables us to predict the production behavior over the life of the well/reservoir. Solutions for more complex situations, such as sources with infinite or finite-conductivity (i.e., a fracture), are provided using discretization of the source. This work considers the case of a complex system with a horizontal well intersecting multiple transverse fractures as an example to show the ability (and flexibility) of the new method. The DVS solution method provides accurate solutions for complex well/fracture configurations — which will help engineers to design and implement optimum well completions. The DVS solutions has been validated by comparing to existing analytical solutions (where applicable), as well as to numerical (simulation) solutions. In all cases the DVS solution was successfully validated — at least in a practical sense — specifically in terms of the accuracy and precision of the DVS solution. As the DVS method is approximate (at early times), there are small discrepancies which are of little or no practical consequence. In terms of computation times, because of its analytic nature, the DVS method is not always optimal in terms of speed for certain problems, but the DVS approach is similar in computation speed with commercial reservoir simulation programs.